Three-dimensional seepage analysis for the tunnel in nonhomogeneous porous media with physics-informed deep learning

Abstract

Tunnel engineering is one of the hot spots of research in the field of geotechnical engineering, and the seepage analysis of tunnels is an important research direction at present. In recent years, physics-informed deep learning based on priori fusion data has become a cross-disciplinary hotspot for solving forward and inverse problems based on partial differential equations (PDEs). In this paper, physics-informed deep learning (PIDL) is introduced to the solution of PDEs for Geotechnical Engineering problems. This paper builds relevant theoretical models and systematically discusses the issues associated with applying this method to the numerical simulation of tunnel seepage, starting from the mathematical theory of physics-informed deep learning. The results of this paper are compared with the analytical solution and the finite element method, and the generalization accuracy of the neural network is tested by replacing different boundary conditions, which verifies the feasibility of the physics-informed deep learning method for solving the seepage problem of tunnels with nonhomogeneous porous media. The results of several typical numerical examples show that the method has the advantages of meshless and refined simulation.